The distance cosines of a line are 1-c- 1-c- 1-c- then

Explanation for the correct answer:Finding the value of c,Given the distance cosines of a line are (1/c, 1/c, 1/c)We know that the sum of the distance of cosine ...

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Standard IX

Mathematics

Finding Ratio of Sides in Triangle When Angles Are Given

The distance ...

Question

The distance cosines of a line are $(\frac{1}{c}, \frac{1}{c}, \frac{1}{c})$ , then

$0 < c < 1$

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$c > 2$

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$c = \pm \sqrt{2}$

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$c = \pm \sqrt{3}$

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$c = \pm 3$

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Solution

The correct option is D
$c = \pm \sqrt{3}$

Explanation for the correct answer:
Finding the value of $c$ ,
Given the distance cosines of a line are $(\frac{1}{c}, \frac{1}{c}, \frac{1}{c})$
We know that the sum of the distance of cosines is equal to $1$
Hence,
${(\frac{1}{c})}^{2} + {(\frac{1}{c})}^{2} + {(\frac{1}{c})}^{2} = 1 \Rightarrow \frac{3}{c^{2}} = 1 \Rightarrow c^{2} = 3 \Rightarrow c = \pm \sqrt{3}$
The value of $c = \pm \sqrt{3}$
Hence, the correct answer is Option (D).

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The distance cosines of a line are 1c,1c,1c, then

The correct option is D c=±3Explanation for the correct answer:Finding the value of c,Given the distance cosines of a line are 1c,1c,1cWe know that the sum of the distance of cosines is equal to 1Hence,1c2+1c2+1c2=1⇒3c2=1⇒c2=3⇒c=±3The value of c=±3Hence, the correct answer is Option (D).

The distance cosines of a line are $(\frac{1}{c}, \frac{1}{c}, \frac{1}{c})$ , then